What is the Universe expanding into..

Do you think there was anything before the big bang?

  • I don't think there was anything before the Big Bang

    Votes: 56 12.5%

  • I think something existed before the Big Bang

    Votes: 200 44.7%

  • I don't think the big bang happened

    Votes: 54 12.1%

  • I think the universe is part of a mutiverse

    Votes: 201 45.0%
  • Total voters
    447
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#8,622
Disco-Pete said:
Talk about MOMENTUM!
Click to expand...

In relation to your ice skater, you have to talk about conservation of angular momentum (L).

Linear momentum, p, is given by the product of mass (m) and velocity (v), and is conserved.

Angular momentum, L, is given bythe product of moment of inertia (I) and angular velocity (w), and is also conserved.

I'm pretty sure I explained the skater scenario to you earlier in the thread.

As the skater draws in her arms, her moment of inertia (the distribution of her mass around the axis of rotation) becomes smaller and so her angular velocity must increase in order to conserve the product, which is angular momentum.
 

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#8,624
I often think that when one encounters an Obstacle in the Evolution of the Universe, one should take a break from it all .🙂

This Man claims to have solved the most Pressing Problem in Mathematics: The Riemann Hypothesis.

https://en.wikipedia.org/wiki/Riemann_hypothesis

TBH, I liked what I saw. 5040 and 7! an' all that.

Looks like a simple proof to me. But surely not that easy. Peer review will surely find a simple error.
 

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#8,629
It is interesting to see how the rotational kinetic energy of the skater changes when she pulls her arms in. Her initial rotational energy is

\[{K}_{\text{Rot}}=\frac{1}{2}I{\omega }^{2},\]


whereas her final rotational energy is

\[{{K}^{\prime }}_{\text{Rot}}=\frac{1}{2}{I}^{\prime }{({\omega }^{\prime })}^{2}.\]

Since

\[{I}^{\prime }{\omega }^{\prime }=I\omega ,\]


we can substitute for

\[{\omega }^{\prime }\]


and find

\[{{K}^{\prime }}_{\text{Rot}}=\frac{1}{2}{I}^{\prime }{({\omega }^{\prime })}^{2}=\frac{1}{2}{I}^{\prime }{(\frac{I}{{I}^{\prime }}\omega )}^{2}=\frac{1}{2}I{\omega }^{2}(\frac{I}{{I}^{\prime }})={K}_{\text{Rot}}(\frac{I}{{I}^{\prime }})\text{}.\]


Because her moment of inertia has decreased,

\[{I}^{\prime }<I,\]


her final rotational kinetic energy has increased. The source of this additional rotational kinetic energy is the work required to pull her arms inward.

This work causes an increase in the rotational kinetic energy, while her angular momentum remains constant.

Since she is in a frictionless environment, no energy escapes the system. Thus, if she were to extend her arms to their original positions, she would rotate at her original angular velocity and her kinetic energy would return to its original value.

Copied from here: https://opentextbc.ca/universityphysicsv1openstax/chapter/11-2-conservation-of-angular-momentum/
 
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#8,630
Galu said:
Any frame of reference in which Newton 1 is valid is an inertial frame.

In what way can an inertial frame change according to the above definition? :scratch1:
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I dong recall saying any of the inertial frames of reference were not valid. Just that if I accelerate an object, I’m shifting its inertial frame of reference from what it was previously to a new inertial frame of reference.
 
#8,632
I can't believe it! The angular momentum of reprocessing my order for that True mirror due to it's "undeliverable" status(assume they broke it), has resulted in a second round of re-rder now expected this Saturday(assume someone now stole it...Prime Member status). There were 3 available, all of which are now in question. If this last one goes missing I'll have to take drastic measures and feel my face like a blind person to discover the difference! Good thing there's the required admiration as Einstein mentions for science to affirm itself, eh! 💋
 
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#8,633
Bonsai said:
When you move something from point A to point B, you accelerate it which simply means you are shifting its inertial frame. Once you remove the force (cease energy expenditure), it occupies a new inertial frame...
Click to expand...

Let's revisit your original statement, Bonsai.

Obviously it is quite permissable for an object to accelerate within an inertial frame (since Newton's second law applies there), but during the acceleration why wouldn't the object stay within that same inertial frame?

Once the accelerating force is removed the object continues to move within the same inertial frame - surely it doesn't now occupy a new inertial frame?
 
#8,636
Galu said:
I've no idea what you are talking about, and I'm not going to google it as I am not a happy bunny!

Your lack of positive feedback to my discussions on the ice skater scenario you introduced dissuades me from answering any more of your questions.

Communication is a two-way process you know.

Sometimes we all need to look in the mirror!
Click to expand...
Huh?

okay,..sure

it's weird that it took you a half hour to lash out..with a response to Bonsai in between.🤪
 
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#8,640
Galu said:
Let's revisit your original statement, Bonsai.

Obviously it is quite permissable for an object to accelerate within an inertial frame (since Newton's second law applies there), but during the acceleration why wouldn't the object stay within that same inertial frame?

Once the accelerating force is removed the object continues to move within the same inertial frame - surely it doesn't now occupy a new inertial frame?
Click to expand...
If an object or objects are coasting through space their IFOR doesn’t change. I used the example of two objects which then had a force acting on one or both. So the IFOR’s between them changed.
 
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